TY - INPR A1 - Nazaikinskii, Vladimir A1 - Savin, Anton A1 - Schulze, Bert-Wolfgang A1 - Sternin, Boris T1 - Elliptic theory on manifolds with nonisolated singularities : III. The spectral flow of families of conormal symbols N2 - When studyind elliptic operators on manifolds with nonisolated singularities one naturally encounters families of conormal symbols (i.e. operators elliptic with parameter p ∈ IR in the sense of Agranovich-Vishik) parametrized by the set of singular points. For homotopies of such families we define the notion of spectral flow, which in this case is an element of the K-group of the parameter space. We prove that the spectral flow is equal to the index of some family of operators on the infinite cone. T3 - Preprint - (2002) 20 KW - elliptic family KW - conormal symbol KW - spectral flow KW - relative index Y1 - 2002 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-26386 ER - TY - INPR A1 - Nazaikinskii, Vladimir A1 - Savin, Anton A1 - Schulze, Bert-Wolfgang A1 - Sternin, Boris T1 - Elliptic theory on manifolds with nonisolated singularities : IV. Obstructions to elliptic problems on manifolds with edges N2 - The obstruction to the existence of Fredholm problems for elliptic differentail operators on manifolds with edges is a topological invariant of the operator. We give an explicit general formula for this invariant. As an application we compute this obstruction for geometric operators. T3 - Preprint - (2002) 24 KW - manifolds with edges KW - edge-degenerate operators KW - elliptic families KW - edge symbol KW - Atiyah-Bott obstruction KW - parameter-dependent ellipticity Y1 - 2002 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-26415 ER - TY - INPR A1 - Nazaikinskii, Vladimir A1 - Savin, Anton A1 - Schulze, Bert-Wolfgang A1 - Sternin, Boris T1 - Elliptic theory on manifolds with nonisolated singularities : II. Products in elliptic theory on manifolds with edges N2 - Exterior tensor products of elliptic operators on smooth manifolds and manifolds with conical singularities are used to obtain examples of elliptic operators on manifolds with edges that do not admit well-posed edge boundary and coboundary conditions. T3 - Preprint - (2002) 15 KW - exterior tensor product KW - edge-degenerate operators KW - elliptic families KW - conormal symbol KW - Atiyah-Bott obstruction Y1 - 2002 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-26335 ER - TY - INPR A1 - Nazaikinskii, Vladimir A1 - Savin, Anton A1 - Schulze, Bert-Wolfgang A1 - Sternin, Boris T1 - Differential operators on manifolds with singularities : analysis and topology : Chapter 5: Manifolds with isolated singularities N2 - Contents: Chapter 5: Manifolds with Isolated Singularities 5.1. Differential Operators and the Geometry of Singularities 5.1.1. How do isolated singularities arise? Examples 5.1.2. Definition and methods for the description of manifolds with isolated singularities 5.1.3. Bundles. The cotangent bundle 5.2. Asymptotics of Solutions, Function Spaces,Conormal Symbols 5.2.1. Conical singularities 5.2.2. Cuspidal singularities 5.3. A Universal Representation of Degenerate Operators and the Finiteness Theorem 5.3.1. The cylindrical representation 5.3.2. Continuity and compactness 5.3.3. Ellipticity and the finiteness theorem 5.4. Calculus of ΨDO 5.4.1. General ΨDO 5.4.2. The subalgebra of stabilizing ΨDO 5.4.3. Ellipticity and the finiteness theorem T3 - Preprint - (2003) 23 Y1 - 2003 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-26659 ER - TY - INPR A1 - Nazaikinskii, Vladimir A1 - Savin, Anton A1 - Schulze, Bert-Wolfgang A1 - Sternin, Boris T1 - Differential operators on manifolds with singularities : analysis and topology : Chapter 7: The index problem on manifolds with singularities N2 - Contents: Chapter 7: The Index Problemon Manifolds with Singularities Preface 7.1. The Simplest Index Formulas 7.1.1. General properties of the index 7.1.2. The index of invariant operators on the cylinder 7.1.3. Relative index formulas 7.1.4. The index of general operators on the cylinder 7.1.5. The index of operators of the form 1 + G with a Green operator G 7.1.6. The index of operators of the form 1 + G on manifolds with edges 7.1.7. The index on bundles with smooth base and fiber having conical points 7.2. The Index Problem for Manifolds with Isolated Singularities 7.2.1. Statement of the index splitting problem 7.2.2. The obstruction to the index splitting 7.2.3. Computation of the obstruction in topological terms 7.2.4. Examples. Operators with symmetries 7.3. The Index Problem for Manifolds with Edges 7.3.1. The index excision property 7.3.2. The obstruction to the index splitting 7.4. Bibliographical Remarks T3 - Preprint - (2004) 06 Y1 - 2004 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-26700 ER -